Target is experiencing a massive backlash from angry customers, with complaints about lack of information and a toll-free number that's reportedly impossible to get through. Some customers have reported problems logging into Target's REDcard credit card website.

The fallout comes a day after Target confirmed about 40 million credit and debit card accounts may have been stolen during a hacking incident that lasted from Nov. 27 to Dec. 15. (If you suspect you may be a victim, read CBS MoneyWatch's article on the next steps to take to protect your accounts.)

Target said it's working with a "leading third-party forensics firm" to investigate the incident. The company also urged customers to call Target at its toll-free number, (866)-852-8680. For customers who have Target-issued REDcards, the company is also urging them to contact the store.

The only problem, according to dozens of complaints on Target's Facebook page, is that it's impossible to get through on the phone. Others wrote that Target's REDcard website was timing out, making it impossible to check if any fraudulent charges had been made.

"Tried several times to call credit card company for Target card," one customer wrote on the company's Facebook page. "Rings then hangs up on you. Finally got through 56 mins on hold then they hung up on me. If you are aware of this issue why wouldn't you get the man power to answer the phones. This is our credit you are talking about."

Other customers had similar complaints, with many writing they were "disappointed," while others vowed to avoid shopping at Target, or to cancel their cards -- as soon as they were able to access their account or reach a customer-service rep.

"How the hell am I suppose to monitor my account if I can't get into it," another customer wrote on Facebook. "No excuse you have is good enough."

For Target, the goodwill of its carefully cultivated brand is at risk. Target, known as a hip, stylish retailer with reasonable prices, has a brand valued at a whopping $25.5 billion, according to global brand consultancy Interbrand. That ranks the retailer as the second most valuable retail brand in the U.S., trailing Wal-Mart.

"In the big picture, there's a cost that goes with responding to the event," such as hiring a forensics investigation, Daren Orzechowski, a partner at White & Case who specializes in information technology legal issues, told CBS MoneyWatch. "But there is a much bigger financial risk that has to do with the loss of goodwill, where consumers might say, 'I won't use my credit card there,' or 'I won't shop there' and go to another big box retailer."

Target spokeswoman Molly Snyder declined to comment on the impact on store sales since the hacking incident was disclosed. The retailer is experiencing higher than normal call volume, and is adding hundreds of staff to its call centers to respond, she told CBS MoneyWatch.

Some customers have complained that Target also didn't release enough information about the security breach, especially concerning whether PIN numbers and the online site were affected.

The company will likely issue updates as it discovers more throughout the course of its investigation, she added.

But it's already too late for some customers. Nomi Waters, whose husband shopped at Target during the security breach timeframe, said she was disappointed with their response.

"Will is affect my decision to shop at Target even though Target is the store that I primarily shop at? YES... screamed with caps! Target has lost the thousands of dollars I spend there every year," Waters wrote in an email to CBS MoneyWatch. "Target knew before they made this announcement that 40 million [people] would be freaking out so how could they not be prepared and have extra call center [people] hired and ready to go?"